Level 5 · Mathematics M5.3

Trigonometric functions

Measure angles in radians, solve trig equations, and prove identities.

Planned. This book is not written yet. Below is its plan, which a teacher can already use.

You are ready for this book if

You can give the exact values of sin 30°, cos 60° and tan 45°.

The plan

  1. M5.3.1 Radians
    • Change between degrees and radians
    • Find arc length and sector area using radians
  2. M5.3.2 The unit circle and any angle
    • Use the unit circle to find sin and cos of any angle
    • Find the sign of sin, cos and tan in each quarter
  3. M5.3.3 Trig graphs and their changes
    • Sketch y = 2 sin 3x and give its period and amplitude
    • Sketch y = tan x and mark its asymptotes
  4. M5.3.4 Solving trig equations
    • Solve sin x = 0.4 for 0 ≤ x ≤ 2π
    • Solve 2cos²x − cos x − 1 = 0
  5. M5.3.5 Identities
    • Use sin²x + cos²x = 1 to simplify an expression
    • Write tan x as sin x divided by cos x
    • Prove a simple trig identity
  6. M5.3.6 Reciprocal and inverse trig functions
    • Sketch the graphs of sec, cosec and cot
    • Use 1 + tan²x = sec²x
    • Give the domain and range of arcsin x
  7. M5.3.7 Compound and double angles
    • Use the formula for sin(A + B)
    • Use double angle formulas to solve an equation
  8. M5.3.8 Combining sin and cos
    • Write 3 sin x + 4 cos x as 5 sin(x + α)
    • Find the largest value of 3 sin x + 4 cos x

For parents and teachers

Level 5 fits learners who can already: read a textbook. use functions and graphs. In many schools that is about 17 to 20, but start wherever the learner is.

Strand: Shape and space. Written and drawn by attnom. Free to read, print and share.